I can't help myself but to reply to this thread. This is the very same reason I picked up an Arduino 3 years ago - to make pretty lights dance to the music all over my house. I'll list every major component you need to get this working. However, you'll have to do some googling, trial and error, and release a bit of magic smoke before you complete this project. That is part of the learning process so do not be put off apparent road blocks. It took me several tries to get what I wanted.
Ok, first- LED strips. You have 2 options here; individual control and single color at a time strips. Individual control is going to cost you about 5 times a much but give a cool effect. For this I would recommend going with WS2801 strips and pixels. Keep in mind that this will also eat up a lot of memory and processor time on the Mega (at least you got the mega- regular Arduino328 would be limited to only one of these strips).
You can score 5 meter strips (with 32 LEDs per meter) from Ebay for less than $90 if you keep an eye out. This particular strip runs at 5 volts. Make sure you watch what voltage – you can get some that run at 12v. Here is an example of 5 volt strip on ebay:
http://www.ebay.com/itm/5m-ws2801-led-digital-strip-32pcs-IC-and-32pcs-5050-SMD-RGB-each-meter-/120984281064?pt=LH_DefaultDomain_0&hash=item1c2b399fe8
You can also mix and match with these WS2801 pixels. They are the same thing just in a strand format:
There is lots of information on these chips on the net – very cheap and popular.
You also have the option to do some accent lighting with cheaper RGB strips that don’t have individual control. Most of these strips run at 12 volts. This is because they are chains of 3 leds together (so you can cut it every 3 leds). You can splice this up into many sections and control them with MOSFETs from the PWM pins on your arduino. A good supplement to individually controlled strips:
And here is a guide on how you’ll need to wire up each segment:
http://www.ladyada.net/products/rgbledstrip/
I really like these strips- I currently have 5 setup in my house ? I cut them to the length of my windows and then stuck them on the top facing up towards the ceiling. This gives a nice diffused effect on the ceiling. I found that pointing the strips right at people’s eyes is less than pleasant.
Audio:
Good choice with that MSQ chip. I won’t write much on that because there’s a wealth of information online. Start by looking here http://www.bliptronics.com/item.aspx?ItemID=116
Power:
You’ll need high quality and strong power supplies. Wall warts won’t cut it for this kind of project. I would also not recommend cheaping out on these. Trust me.
I have had great experience with the RS series of power supplies from meanwell: http://www.trcelectronics.com/Meanwell/power-supply-rs.shtml
You can get these in a variety of voltage and amperage ratings to meet your needs.
When I first started I tried to run everything off of 1 old ATX power supply. This works but really is a pain running wires all over the place. Instead I settled with using multiple power supplies that were smaller and located close to what they were powering. This made my life quite a bit easier and performance was better. Remember to have a common ground if you do this.
If I recall, the 5v strips need about 3 amps per 5 meters and the 12v strips need about 2. However, you want to round up here.
For a single 12v 5m strip get a RS-25-12. For a single 5v strip get a RS-25-5. If you want to run 2 or 3 5v strips for example you can simply get a single RS-50-5. Same for the 12v stuff. When you wire these you’ll have the power and ground go to the strip, and also the ground tied to the ground on the Arduino (not the power!).
Supplies:
If you have a nice soldering station you’ll have a great time. At the very least make sure you have thin solder and a good fresh tip. Also make sure to get some high quality wire to run to each of your strips. I preferred to use Cat6 Ethernet for this. Make sure you get stranded copper and not solid copper! Your life will be easier with the stranded stuff.
Let me know if you have any other questions – but remember that experimentation is the way you really learn how this stuff works. Make sure to keep us updated with your project! Lots of pictures plz 
Cheers,
Brian